Thermodynamic consistency of liquid-gas lattice Boltzmann simulations

TL;DR

This paper analyzes the thermodynamic consistency of liquid-gas lattice Boltzmann simulations and introduces a forcing method to ensure true equilibrium solutions with consistent chemical potential and pressure.

Contribution

The paper provides a higher-order equilibrium analysis of non-ideal lattice Boltzmann methods and proposes a new forcing technique for thermodynamic consistency.

Findings

Identification of higher order terms causing thermodynamic inconsistency

Development of a thermodynamically consistent forcing method

Improved equilibrium solutions with constant chemical potential and pressure

Abstract

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to consistently derive the fourth order terms that are necessary to represent an extended interface. These same terms are also responsible for thermodynamic consistency, i.e. to obtain a true equilibrium solution with both a constant chemical potential and a constant pressure. In this article we present an equilibrium analysis of non-ideal lattice Boltzmann methods of sufficient order to identify those higher order terms that lead to a lack of thermodynamic consistency. We then introduce a thermodynamically consistent forcing method.